The \(1s\rightarrow np\)  resonance peaks occur for \(3\hbar \omega =E_{1s\rightarrow np}\) , while the \(1s\rightarrow ns\)  and \(1s\rightarrow nd\)  peaks are situated at \(3\hbar \omega =\frac{3}{2}E_{1s\rightarrow ns/nd}\) . Additionally, the peak at \(3\hbar \omega = 87.1727\,\mathrm {meV}\)  corresponds to \(3\hbar \omega =3E_{1s\rightarrow 2p}\) . This is due to the response at both \(2\omega \)  [1]} and \(\omega \)  also being present in this process, described in detail in Section 3.2 of [2]}, i.e. \(2\hbar \omega =E_{1s\rightarrow ns/nd}\)  and \(\hbar \omega =E_{1s\rightarrow 2p}\) . No other peaks for \(\hbar \omega =E_{1s\rightarrow np}\)  are visible, as they would already be outside the considered frequency domain (\(3E_{1s\rightarrow 3p}\sim 105.872\,\mathrm {meV}\) , barely outside of the plot).
